In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias ((I1/I2)) will be x: 1. The value of x will be

Question

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias ((I1/I2)) will be x: 1. The value of x will be (A)  (B)  (C)  (D)

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/545ee32c44b87c9e9dbdeb333a946eb9-.png" /> (1/2) I1(ω1)2=(1/2) I2(ω2)2 I1((v/3 R))2=I2((v/R))2 (I1/I2)=(9/1)

Q. In the given figure, two wheels $P$ and $Q$ are connected by a belt $B$ . The radius of $P$ is three times as that of $Q$ . In case of same rotational kinetic energy, the ratio of rotational inertias $(\frac{I _{1}}{I _{2}})$ will be $x : 1$ . The value of $x$ will be____

$\frac{1}{2} I_{1} (ω_{1})^{2} = \frac{1}{2} I_{2} (ω_{2})^{2}$
$I_{1} (\frac{v}{3 R})^{2} = I_{2} (\frac{v}{R})^{2}$
$\frac{I _{1}}{I _{2}} = \frac{9}{1}$

Q. In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias (I2​I1​​) will be x:1. The value of x will be____

21​I1​(ω1​)2=21​I2​(ω2​)2 I1​(3Rv​)2=I2​(Rv​)2 I2​I1​​=19​

Q. In the given figure, two wheels $P$ and $Q$ are connected by a belt $B$ . The radius of $P$ is three times as that of $Q$ . In case of same rotational kinetic energy, the ratio of rotational inertias $(\frac{I _{1}}{I _{2}})$ will be $x : 1$ . The value of $x$ will be____

$\frac{1}{2} I_{1} (ω_{1})^{2} = \frac{1}{2} I_{2} (ω_{2})^{2}$
$I_{1} (\frac{v}{3 R})^{2} = I_{2} (\frac{v}{R})^{2}$
$\frac{I _{1}}{I _{2}} = \frac{9}{1}$